Internal problem ID [3895]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 6
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {u^{\prime }+b u^{2}-\frac {c}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 39
dsolve(diff(u(x),x)+b*u(x)^2=c*x^(-4),u(x), singsol=all)
\[ u \relax (x ) = -\frac {\sqrt {-c b}\, \tan \left (\frac {\sqrt {-c b}\, \left (c_{1} x -1\right )}{x}\right )-x}{b \,x^{2}} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 125
DSolve[u'[x]+b*u[x]^2==x^(-4),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {\left (x+\sqrt {-b} c_1\right ) \cosh \left (\frac {\sqrt {b}}{x}\right )-\frac {\left (b+\sqrt {-b} c_1 x\right ) \sinh \left (\frac {\sqrt {b}}{x}\right )}{\sqrt {b}}}{b x^2 \left (\cosh \left (\frac {\sqrt {b}}{x}\right )-c_1 \sin \left (\frac {\sqrt {-b}}{x}\right )\right )} \\ u(x)\to \frac {x-\sqrt {b} \coth \left (\frac {\sqrt {b}}{x}\right )}{b x^2} \\ \end{align*}